A non-isothermal transient flow of gas/condensate in pipelines is discussed. The main objective of the model is to predict the distribution of major parameters along the pipeline. Two-fluid model coupled with dispersed with uniform droplet size flow regime is used to describe the flow. A non-isothermal condition is incorporated to the model through energy equations written for each phase. Energy and mass transfer between the phases are taken into consideration and regarded as a source/sink terms in phases' equations. Inertia terms in the phases' momentum equations are also included. An explicit, five-point, second-order accurate total variation diminishing (TVD) scheme is formulated to solve the system of governing equations. Special attention is given to the treatment of boundary conditions at inlet and outlet of the pipeline. TVD scheme is found to preserve the shock adequately, with small dispersion effect. The obtained results are found to be quantitatively descriptive; however, they can not be quantified because of the lack of experimental data.